Connect a loop of edges to a point
You can do a couple of things:


In edit mode, select the Ngon, and triangulate it. (CtrlT )
Or Poke the face to create a fan (AltP)
Select all the faces you would like to flatten, for an average, or the one you would like the others to match, and create a new Transform Orientation (CtrlAltSpace). Perhaps give it a name. Then, making sure you're in your new orientation,  with the faces you want to be planar selected, scale them to 0 along your newly created Z-axis (SZZ0)